Question

if a sequence has a common ratio of 0.5, what will happen to its terms? a. the sequence will alternate. b. the sequence will shrink gradually. c. the sequence will remain constant. d. the sequence will grow.

Explanation:

Step1: Recall geometric - sequence property

For a geometric sequence with common ratio \(r\), if \(|r|< 1\), the terms of the sequence shrink.

Step2: Analyze the given common ratio

Here, the common ratio \(r = 0.5\) and \(|0.5|=0.5<1\). So the terms of the sequence will shrink gradually.

Answer:

b. The sequence will shrink gradually.